SAMS Subject Classification Number: 13

In this talk, we study Bourbaki-boundedness on quasi-pseudometric spaces. It turns out that if a set is Bourbaki-bounded on the symmetrized quasi-pseudometric space, then it is Bourbaki-bounded in the quasi-metric space but the converse need not to be true. We show that an asymmetric normed space is Bourbaki-bounded if and only if it is bounded. Consequently, we prove that every real-valued semi-Lipschitz in the small function on a quasi-metric space is bounded if and only if the quasi-metric is Bourbaki-bounded.

[1] G. Beer and M.I. Garrido, Bornologies and locally lipschitz functions, Bull. Aust. Math. Soc. 90 (2014), 257–263.

[2] O. Olela Otafudu and D. Mukonda, On Bourbaki-bounded sets on quasi-pseudometric spaces, Math. Appl. (To appear)

[3] O. Olela Otafudu, W. Toko and D. Mukonda, On bornology of extended quasi-metric spaces, Hacet. J. Math. Stat. 48 (2019), 1767–1777.